was used in the classical reference [1]}.
It is easy to see that \(L_r(\lambda )\)  is a linear polynomial system matrix of \(P(\lambda )\) , since \(P(\lambda ) = D_r(\lambda ) + C_r (\lambda ) A_r (\lambda )^{-1} B_r (\lambda )\) , and that it
is minimal for all finite \(\lambda \) . For the point at \(\infty \) , E-controllability is clearly satisfied but E-observability is only satisfied if the matrix \(P_d\)  has full column rank \(n\) . Thus, \(L_r (\lambda )\)  is not a strongly minimal linearization of \(P(\lambda )\)  when \(P_d\)  does not have full column rank. However, note that \(L_r (\lambda )\)  is always a GLR-strong linearization of \(P(\lambda )\) . This can be seen, for instance, by noting that if the two block rows in (REF ) are interchanged, we obtain one of the block Kronecker linearizations (with only one block column) associated to \(P(\lambda )\)  defined in [2]}. The pencil (REF ) has a structure similar to that of the classical first or row Frobenius companion form.
